gevstat

Generalized extreme value mean and variance

Syntax

m = gevstat(k,sigma,mu)

[m,v] = gevstat(k,sigma,mu)

Description

m = gevstat(k,sigma,mu) returns the mean for the generalized extreme value (GEV) distribution defined by the shape parameter k, scale parameter sigma, and location parameter mu.

When k < 0, the GEV distribution is the type III extreme value distribution. When k > 0, the GEV distribution is the type II (Frechet) extreme value distribution. If w has a Weibull distribution, then –w has a type III extreme value distribution and 1/w has a type II extreme value distribution. In the limiting case as k approaches 0, the GEV distribution is the mirror image of the type I (Gumbel) extreme value distribution. For more information, see Generalized Extreme Value Distribution.

[m,v] = gevstat(k,sigma,mu) also returns the variance for the distribution.

Examples

Compute Mean and Variance

Compute the mean and variance of a generalized extreme value distribution with the shape parameter k, scale parameter sigma, and location parameter mu.

k = 0.1;
sigma = 2;
mu = 3;
[mean,variance] = gevstat(k,sigma,mu)

mean = 
4.3726

variance = 
8.9050

Input Arguments

k — Shape parameter

scalar value | array of scalar values

Shape parameter, specified as a scalar value or an array of scalar values. If one or more of the input arguments k, sigma, and mu are arrays, then the array sizes must be the same. In this case, gevstat expands each scalar input into a constant array of the same size as the array inputs.

Data Types: single | double

sigma — Scale parameter

positive scalar value | array of positive scalar values

Scale parameter, specified as a positive scalar value or an array of positive scalar values. If one or more of the input arguments k, sigma, and mu are arrays, then the array sizes must be the same. In this case, gevstat expands each scalar input into a constant array of the same size as the array inputs.

Data Types: single | double

mu — Location parameter

scalar value | array of scalar values

Location parameter, specified as a scalar value or an array of scalar values. If one or more of the input arguments k, sigma, and mu are arrays, then the array sizes must be the same. In this case, gevstat expands each scalar input into a constant array of the same size as the array inputs.

Data Types: single | double

Output Arguments

m — Mean

numeric scalar | array of numeric scalars

Mean for the GEV distribution, returned as a numeric scalar or an array of numeric scalars. m is the same size as k, sigma, and mu. Each element in m is the mean of the GEV distribution specified by the corresponding elements in k, sigma, and mu.

The mean of the GEV distribution is not finite when k ≥ 1.

v — Variance

numeric scalar | array of numeric scalars

Variance for the GEV distribution, returned as a numeric scalar or an array of numeric scalars. v is the same size as k, sigma, and mu. Each element in v is the variance of the GEV distribution specified by the corresponding elements in k, sigma, and mu.

The variance of the GEV distribution is not finite when k ≥ 1/2.

References

[1] Embrechts, P., C. Klüppelberg, and T. Mikosch. Modelling Extremal Events for Insurance and Finance. New York: Springer, 1997.

[2] Kotz, S., and S. Nadarajah. Extreme Value Distributions: Theory and Applications. London: Imperial College Press, 2000.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a